Which statement about a CDF is true?

• A. A CDF is always decreasing.
• B. A CDF is nondecreasing and approaches 1 as x increases.
• C. A CDF can take negative values.
• D. A CDF is defined only for discrete variables.

Answer: (B)

The main idea is that a CDF records the probability that the random variable is at most x, so when x grows, you’re including more possible outcomes. That makes the CDF nondecreasing: as you move to larger x, F(x) does not go down. As x grows larger and larger, you eventually include all possible outcomes, so F(x) approaches 1. The CDF always stays between 0 and 1, and it applies to any distribution, whether discrete, continuous, or mixed. It cannot be decreasing, cannot take negative values, and it isn’t limited to discrete variables.